Some Republican leaders have gently urged King not to run for Senate. But they concede there's little they can do, given King's tea party support and an Iowa Republican Party organization that's largely run by allies of libertarian hero Ron Paul.

"It's a total free-for-all," said Doug Gross, a fundraiser allied with GOP Gov. Terry Branstad.

The new Rove-affiliated PAC may be able to pour millions of dollars into selected primaries. That could buy a lot of TV ads, mailings and ground troops. But history shows it's often hard for party leaders to control primaries, which tend to be dominated by ideological voters.

Establishment favorite Mike Castle, for instance, spent heavily in the 2010 Delaware Senate primary, but tea party activist Christine O'Donnell prevailed. She then lost to a Democrat who was considered a near-certain loser to Castle.

Tea party activists note that some prominent mainstream Republicans also have lost competitive Senate races, including those last fall in North Dakota and Montana.

Democrats struggle with primaries as well. Obama and other top Democrats tried to clear the Pennsylvania Senate nomination for Republican-turned-Democrat Arlen Specter in 2010, warning congressman Joe Sestak he'd be crushed if he challenged Specter. Pennsylvania Democrats nominated Sestak, who lost to Republican Pat Toomey.

In another sign of Republican soul-searching Tuesday, House Majority Leader Eric Cantor said the party must show voters that it cares about education, health care and immigration changes in addition to the deficits and spending cuts it dwells on so often.

In a speech in Washington, Cantor, R-Va., said federal aid should be available for students hoping to move to charter or private schools to escape poorly performing public schools. He also said the government should continue funding medical research.

Cantor said hourly workers should be allowed to "convert previous overtime into future comp-time or flex-time" to care for children or other family needs.

And in a shift in position, Cantor said illegal immigrants who came to the country as children should be given a pathway to citizenship.

Meanwhile, the nation's only two Hispanic governors signaled they will lead an expanded Republican effort to recruit Latino and female candidates for state offices across the country. The Republican State Leadership Committee planned a conference call Wednesday with New Mexico Gov. Susana Martinez and Nevada Gov. Brian Sandoval to announce the formation of the Future Majority Caucus.

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Associated Press writers Thomas Beaumont in Iowa, Russell Contreras in New Mexico and Bill Barrow in Georgia contributed to this report.